Mr Horta-Osorio stressed that TSB, which will be launched on Monday, was a "completely clean bank".

It had no legacy issues - such as a huge bill from PPI compensation - and had the same protection for savers as other High Street banks.

Collapsed deal

Lloyds was ordered to sell the branches by the European Commission. The sale was a condition of the government's bail-out for the bank, which is 39%-owned by the taxpayer.

The plan to sell them is known as Project Verde.

This is the cosmetic part of a more fundamental process of breaking up Lloyds, ordered by the European Commission, to create a bit more choice for customers and more competition for the UK's giant banks

The Co-op Bank became the preferred bidder to buy the Lloyds branches - under the TSB brand - in December 2011, but the deal fell through in April this year.

Instead, Lloyds is planning to float TSB on the stock market in the middle of next year.

Switching accounts

On Monday, the bank will be operating independently on the High Street, with the branches being rebranded, letterheads being changed, and a new website ready to operate.

Customers of the 631 branches that will be transferred to TSB had no choice in seeing their accounts move to the new TSB brand. They received letters by the turn of the year explaining what would happen, but some have still voiced their frustration and confusion.

However, Mr Horta-Osorio told the BBC's business editor, Robert Peston, that it would be a "seamless transition for customers".

"The only change that customers will notice is the change of the name," he said.

Customers' bank account numbers and sort codes will remain the same. No-one's cards will stop working. The cards will simply be reissued with a new name for the bank, in due course.

Reviving the TSB brand name

The new bank will be called TSB and operate independently

The name is drawn from the movement of savings banks that began in 1810

The first was set up for working people in Ruthwell, Dumfriesshire. When it began, no withdrawals could be made without the approval of the trustees

The savings bank movement grew, with deposits hitting £1bn for the first time in 1951

"If customers want, after the transaction is closed, they can close their accounts with TSB and move to Lloyds, or they can close their accounts with Lloyds and go to TSB, either of the two," Mr Horta-Osorio added.

However, he said there had been very few customers expressing a wish to switch.

Saver protection

Despite the reassurance for customers, Mr Horta-Osorio said that this was a huge project for Lloyds Banking Group, costing between £1.3bn and £1.5bn before tax.

He said the new TSB represented about a sixth of Lloyds' customer base and branch network. It would have about the same number of branches as the Halifax, which is part of the Lloyds Banking Group.

The legal entity of TSB is already in place, with a banking licence. That means that £85,000 of savings per customer is protected under the Financial Services Compensation Scheme, were the institution to go bust - as with all other UK-registered banks.

The TSB name has been revived after being merged with Lloyds in 1995. The branches that are moving are those of the former Cheltenham & Gloucester building society and of Lloyds TSB Scotland, as well as a cross-section of Lloyds branches in England and Wales.

In a wide-ranging interview, Mr Horta-Osorio admitted that "leadership is a lonely thing". He had to take some time off in 2011, on doctors' orders, owing to the exhaustion of the stress of turning Lloyds around.

He also said that the bank, which has a registered office and large operation in Scotland, was carefully monitoring the situation if there was a vote for independence in Scotland.